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<p><code>#include &lt;<a class="el" href="symmetric__rep_8h_source.html">symmetric_rep.h</a>&gt;</code></p>
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Public Types</h2></td></tr>
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typedef <a class="el" href="classcSymmetricRep.html">cSymmetricRep</a>&lt; T &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>SelfType</b></td></tr>
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Public Member Functions</h2></td></tr>
<tr class="memitem:a64f4c25b8f5aebbd78f49f3485aed88f"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcSymmetricRep.html#a64f4c25b8f5aebbd78f49f3485aed88f">cSymmetricRep</a> (std::vector&lt; T &gt; &amp;generators_set)</td></tr>
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&#160;</td><td class="memItemRight" valign="bottom"><b>cSymmetricRep</b> (const <a class="el" href="classcSymmetricRep.html">SelfType</a> &amp;sym_rep)</td></tr>
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<a class="el" href="classcSymmetricRep.html">cSymmetricRep</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><b>operator=</b> (const <a class="el" href="classcSymmetricRep.html">SelfType</a> &amp;sym_rep)</td></tr>
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<tr class="memitem:a60f095284b40e494a34fda76e1fc7ecd"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcSymmetricRep.html#a60f095284b40e494a34fda76e1fc7ecd">Contains</a> (const T &amp;element) const </td></tr>
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<tr class="memitem:a935cec1dbd90a09581f1aa7f150eb9de"><td class="memItemLeft" align="right" valign="top">std::vector&lt; T &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcSymmetricRep.html#a935cec1dbd90a09581f1aa7f150eb9de">GetElementsNaive</a> () const </td></tr>
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<tr class="memitem:ad9f112b996c14824bd1d669aed162cbf"><td class="memItemLeft" align="right" valign="top">std::vector&lt; T &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcSymmetricRep.html#ad9f112b996c14824bd1d669aed162cbf">GetElementsDimino</a> () const </td></tr>
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<tr class="memitem:a62cbd7057456f503eec43d592497e94f"><td class="memItemLeft" align="right" valign="top">std::vector&lt; std::size_t &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcSymmetricRep.html#a62cbd7057456f503eec43d592497e94f">GetOrbit</a> (const std::size_t &amp;set_element) const </td></tr>
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const std::vector&lt; T &gt; &amp;&#160;</td><td class="memItemRight" valign="bottom"><b>GetGeneratorsSet</b> () const </td></tr>
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void&#160;</td><td class="memItemRight" valign="bottom"><b>SetGeneratorsSet</b> (const std::vector&lt; T &gt; &amp;gen_set)</td></tr>
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void&#160;</td><td class="memItemRight" valign="bottom"><b>AddGenerator</b> (const T &amp;element)</td></tr>
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void&#160;</td><td class="memItemRight" valign="bottom"><b>ClearGenerators</b> ()</td></tr>
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bool&#160;</td><td class="memItemRight" valign="bottom"><b>operator==</b> (const <a class="el" href="classcSymmetricRep.html">SelfType</a> &amp;symgrp) const </td></tr>
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bool&#160;</td><td class="memItemRight" valign="bottom"><b>operator!=</b> (const <a class="el" href="classcSymmetricRep.html">SelfType</a> &amp;symgrp) const </td></tr>
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T&#160;</td><td class="memItemRight" valign="bottom"><b>GetIdentity</b> () const </td></tr>
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<tr class="memitem:a2dfa5d3358d69914a625536d994be72c"><td class="memItemLeft" align="right" valign="top">std::vector&lt; T &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcSymmetricRep.html#a2dfa5d3358d69914a625536d994be72c">GetCyclicSubgroupEl</a> (const T &amp;element) const </td></tr>
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<tr class="memitem:ac110028d8d6e161448f15bc1548d5274"><td class="memItemLeft" align="right" valign="top">std::vector&lt; T &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcSymmetricRep.html#ac110028d8d6e161448f15bc1548d5274">GetCyclicSubgroupEl</a> (const std::size_t size)</td></tr>
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<tr class="memitem:a4a9724dc8ba8c8ccc041fe1f86dc4701"><td class="memItemLeft" align="right" valign="top">std::vector&lt; T &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classcSymmetricRep.html#a4a9724dc8ba8c8ccc041fe1f86dc4701">GetDihedralSubgroupEl</a> (const std::size_t size)</td></tr>
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Private Attributes</h2></td></tr>
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std::vector&lt; T &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>m_GenSet</b></td></tr>
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Friends</h2></td></tr>
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std::ostream &amp;&#160;</td><td class="memItemRight" valign="bottom"><b>operator&lt;&lt;</b> (std::ostream &amp;out, const <a class="el" href="classcSymmetricRep.html">SelfType</a> &amp;group_rep)</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template&lt;typename T&gt;<br/>
class cSymmetricRep&lt; T &gt;</h3>

<p>symmetric group internal representation class used only from <a class="el" href="classcGroup.html">cGroup</a> TODO &ndash; add elements member + GetElements method (cache) </p>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
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          <td>(</td>
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<p>constructs object from a vector of permutations </p>

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          <td>(</td>
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<p>constructs object from an intializer list of permutations </p>

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<h2 class="groupheader">Member Function Documentation</h2>
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<p>returns true if it finds the element in the elements obtained by running Dimino's algorithm </p>

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Here is the call graph for this function:</div>
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<p>returns the cyclic subgroup elements generated by the given element by computing it's powers until identity is reached Complexity: O(n), where n is the order of the element </p>

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<p>returns the cyclic subgroup $C_n$ elements by rotating the identity permutation of the given size Complexity $O(n)$, where n is the size given as parameter </p>

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<p>returns the dihedral subgroup $D_2n$ = $C_n + R_n$, where $R_n$ is generated rotating by a fundamental reflection Complexity $O(2n)$, where n is the size of the symmetry n-gon </p>

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<p>returns the group elements by performing the Dimino algorithm TODO - Complexity: see Butler - "Fundamental Algorithms for permutation groups" </p>

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<p>returns the set of elements by trying to generate all combinations Complexity: O(n^2*m), where n is the number of elements and m is the number of generators TODO - by improving the data structure we could improve the find operation see Butler - "Fundamental Algorithms for permutation groups" </p>

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<p>returns the orbit of a set element(the images of the elements under the group elements) Complexity: O(n^2*m) where n is the size of the orbit and m is the order of the group </p>

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<hr/>The documentation for this class was generated from the following file:<ul>
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